New efficient numerical method for 3D point cloud surface reconstruction by using level set methods

Abstract

In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the calculation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency is a construction of initial condition by a simple tagging algorithm which allows us also to highly speed up the numerical scheme when solving PDEs. For the numerical discretization of the model we suggested a novel unconditionally stable method, in which the semi-implicit co-volume scheme is used in curvature part and implicit upwind scheme in advective part. The method was tested on representative examples and applied to real data representing the historical and cultural objects scanned by 3D laser scanners.